We study a Brownian motor moving in a sawtooth potential in the presence of an external driving force and two heat reservoirs.Based on the corresponding Fokker-Planck equation,the analytical expressions of the current and efficiency in the quasi-steady-state limit are obtained.The effects of temperature difference and the amplitude of the external driving force on the current and efficiency are discussed,respectively.The following is our findings.（i） The current increases with both δ and A.In other words,δ and A enhance the transport of the Brownian motor.（ii） The competition between the temperature difference and the amplitude of the external driving force can lead to efficiency optimization.The efficiency is a peaked function of temperature,i.e.,δ 0 and a lower amplitude value of the external driving force is necessary for efficiency optimization.（iii） The efficiency increases with δ,and decreases with A.δ and A play opposite roles with respect to the efficiency,which indicates that δ enhances the efficiency of energy transformation while A weakens it.
For the activated dynamics of a Brownian particle moving in a confined system with the presence of entropic barriers, this paper investigates a periodic driving and correlations between two noises. Within the two-state approximation, the explicit expressions of the mean first passage time （MFPT） and the spectral power amplification （SPA） axe obtained, respectively. Based on the numerical computations, it is found that： （i） The MFPT as a function of the noise intensity exhibits a maximum with the positive correlations between two noises （λ〉0）, this maximum for MFPT shows the characteristic of the entropic noise induced stability （ENIS） effect. The intensity A of correlations between two noises can enhance the ENIS effect. （ii） The SPA as a function of the noise intensity exhibits a double-peak by tuning the noise correlation intensity λ, i.e., the existence of a double-peak behaviour is the identifying characteristic of the double entropic stochastic resonance phenomenon.
In this paper, we investigate the escape of Brownian particles and stochastic resonance (SR) with low-temperatures quantum fluctuations by using the quantum Smoluchowski equations at low-temperature. Two specific examples have been considered: one is the example of bistable system, and the other is the example of metastable system. The explicit expressions of the mean-first passage time (MFPT) and signal-to-noise ratio (SNR) for both specific examples are obtained, respectively. Based on the numerical computations, we compare the quantum case with its classical counterpart. Our research results show that: (i) the quantum effect accelerates the escape of the Brownian particle in comparison with the classical result and (ii) the quantum effect enhances the SR in the SNR as a function of β for a bistable system (i.e., β = 1/kBT, kB is the Boltzmann constant and T is the temperature), while for a metastable system, the β amplifies the quantum effects, and the quantum effect weakens the SNR as a function of β.
The transient properties of a three-level atomic optical bistable system in the presence of multiplicative and additive noises are investigated. The explicit expressions of the mean first-passage time （MFPT） of the transition from the high intracavity intensity state to the low one are obtained by numerical computations. The impacts of the intensities of the multiplicative noise DM and the additive noise DA, the intensity of correlation between two noises λ, and the intensity of the incident light y on the MFPT are discussed, respectively. Our results show： （i） for the case of no correlation between two noises （2, = 0.0）, the increase in DM and DA can lead to an increase in the probability of the transition to the low intracavity intensity state, while the increase in y can lead to a retardation of the transition; and （ii） for the case of correlation between two noises （λ≠ 0.0）, the increase in λ can cause an increase in the probability of the transition, and the increase in DA can cause a retardation of the transition firstly and then an increase in the probability of the transition, i.e., the noise-enhanced stability is observed for the case of correlation between two noises.
